Question

РОЗВ'ЯЖІТЬ РІВНЯННЯ 1. 3х(3х-5)-(2х-5)²=(2х+1)(2х-1) 2. -0,2х²+х+10=0

Answer 1

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Answer 2

Ответ:

Ответ на фото.

Answer 3

1. 3x(3x-5)-(2x-5)²=(2x+1)(2x-1)

Let's simplify the equation step by step:

Expanding the squared term: 3x(3x-5) - (4x² - 20x + 25) = (2x+1)(2x-1)

Multiplying 3x by each term inside the parentheses: 9x² - 15x - 4x² + 20x - 25 = (2x+1)(2x-1)

Combining like terms: (9x² - 4x²) + (-15x + 20x) - 25 = (2x+1)(2x-1)

Simplifying further: 5x² + 5x - 25 = (2x+1)(2x-1)

Expanding the right side: 5x² + 5x - 25 = 4x² - 1

Moving all terms to one side: 5x² + 5x - 25 - 4x² + 1 = 0

Combining like terms: x² + 5x - 24 = 0

Now we have a quadratic equation. We can solve it by factoring or using the quadratic formula.

Factoring: (x + 8)(x - 3) = 0

Setting each factor equal to zero: x + 8 = 0 or x - 3 = 0

Solving for x: x = -8 or x = 3

Therefore, the solutions to the equation are x = -8 and x = 3.

2. -0.2x² + x + 10 = 0

To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this equation, a = -0.2, b = 1, and c = 10.

Substituting the values into the quadratic formula: x = (-(1) ± √((1)² - 4(-0.2)(10))) / (2(-0.2))

Simplifying further: x = (-1 ± √(1 + 8)) / (-0.4)

x = (-1 ± √9) / (-0.4)

x = (-1 ± 3) / (-0.4)

We have two possibilities:

1. x = (-1 + 3) / (-0.4) x = 2 / (-0.4) x = -5

2. x = (-1 - 3) / (-0.4) x = -4 / (-0.4) x = 10

Therefore, the solutions to the equation are x = -5 and x = 10.